APPLETON, Wis. The election may be only a month away, but that doesn't mean Brenda Hansen wants to have a conversation about politics.

"Nobody says the P word," said Hansen, who lives an hour south of Green Bay. "You talk about football, you talk about baseball. People even are talking about the weather. We're talking about what we're buying for Christmas. Just not politics."

It's easy to understand why. Over the past two years, Wisconsin has emerged as perhaps the best illustration of just how polarized the American political landscape has become. That's due in large part to Republican Gov. Scott Walker's attempt to pass legislation curbing the bargaining power of public sector unions after his 2010 election, which set off a protracted battle that included angry protests in the capital and a failed recall attempt in June.

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"I'm so sick of politics after the whole governor fiasco," said Hansen's friend Kelly Abel of Appleton. "This past year, two years, has just been politics. I'm sick of hearing everything."

She's going to have to endure it a little bit longer. Wisconsin has emerged as one of the key battleground states in the presidential election, thanks in part to Mitt Romney's decision to tap Wisconsin Rep. Paul Ryan as his running mate. A Quinnipiac University/CBS News/New York Times pollout Thursday showed the race to be effectively a tossup: President Obama leads Romney 50 percent to 47 percent in the battle for the state's 10 electoral votes. The Obama campaign is clearly spooked: Mr. Obama has visited the state twice over the past month, including a stop in the Democratic stronghold of Madison right after the first presidential debate. Vice President Joe Biden and first lady Michelle Obama have also made campaign trips to the state over the past two months. And the Obama campaign started running ads in the state in September.

In light of Mr. Obama's 14-point Wisconsin victory four years ago, one might think that the Obama campaign shouldn't have needed to go to the trouble. But Wisconsin is a more divided state than the 2008 election suggests: Though a Republican hasn't won here since Ronald Reagan's landslide victory in 1984, Wisconsin came within a half point of going to George W. Bush in both 2000 and 2004. The Badger State may be home to liberal bastions like Madison and liberal politicians like former Sen. Russ Feingold and Senate candidate Tammy Baldwin, but it's also the land of Walker, Ryan, Republican National Committee chair Reince Priebus and the GOP stronghold of Waukesha County, which supported McCain over Mr. Obama by a 26 point margin.

And while Democrats are seen as having an organizational advantage in most of the battleground states, Wisconsin is an exception thanks to the expensive Walker recall fight. Last month, Obama campaign manager Jim Messina acknowledged that Republicans "test drove their car [in Wisconsin] whereas in other states they haven't."

"It would make sense they're strong here, as are we," he said. "They are stronger than McCain was in '08, no question, on the ground."

A victory in Wisconsin would give Romney some very important breathing room in getting to the 270 electoral votes necessary to win the presidency. Even after the boost he got following the first presidential debate, Romney has a relatively narrow path to 270. Winning Wisconsin would mean he could afford to lose states like Iowa and New Hampshire; it would also give him a plausible path to victory that does not include Ohio's 18 electoral votes. If Romney loses Wisconsin and Ohio, he would have to complete a near-sweep of the other seven battleground states to secure a victory.

The Ryan effect

Wisconsin Republicans say that Romney's decision to tap Ryan, who faced off at the vice presidential debate against Joe Biden on Thursday night, has energized their side. "What Paul Ryan being on the ticket does is add to our voter enthusiasm," says a Romney campaign official in Wisconsin. "And enthusiasm is what wins races."

That enthusiasm could be seen at the Rochester Deli in Waukesha, where Dan Trawicki, who works in law enforcement, said he was backing what he referred to as the "Romney-Ryan ticket."

"I think Paul Ryan is one of the first elected officials to speak openly and honestly about some of the entitlements that are there, that we're in trouble," he said.

It's not clear that Ryan's roots will sway many Wisconsin voters, however. The landscape has changed since John F. Kennedy tapped Texan Lyndon Johnson as his running mate in 1960 in order to win Texas and other Southern states, says University of Wisconsin-Madison professor Kenneth Mayer.

"There isn't a whole lot of evidence that a vice presidential nomination can make a non-competitive race competitive today," he said. "But at the same time - a vice presidential nominee from a state can add a couple of percentage points." And with the candidates now separated by just three percentage points, that could be enough to swing the race.

Democrats are quick to point out that Ryan simply wasn't all that well known statewide before he was tapped by Romney - one July survey found that more than a third of Wisconsinites said they did not have enough information about him to say whether they had a favorable impression. "At this point, you'd be hard-pressed to make the argument that he's helping Romney anywhere but his own congressional district," said an Obama campaign official in Wisconsin. "He only represented one part of the state, he passed on a statewide run."

Carol Smith, a conservative Romney supporter who lives in Waukesha County, said that while she was "thrilled" that Ryan was picked, she doesn't think the choice is going to have a significant impact on most voters in the state.

"I think it made a difference in some early enthusiasm, but I don't know," she said. "Maybe for some swing voters. But people who are going to vote for Romney are going to vote for him anyway."